Development and performance evaluation of a high‐speed multileaf collimator

Abstract Multileaf collimator (MLC) tracking represents a promising technique for motion management in radiotherapy. However, the conflict between limited leaf speed/acceleration and the demand for tracking fast target motion is now a prominent issue. Conventional MLCs typically have a maximum leaf speed of 3–4 cm/s and a maximum leaf acceleration of 50–70 cm/s2, which are inadequate to track fast target motion. To cope with this problem, we have recently developed a high‐speed multileaf collimator (HS‐MLC) prototype, which employs linear motors instead of rotary motors to drive leaves. Consequently, it inherits various benefits of linear motors, including direct drive and high dynamics. The primary aim of this paper was to introduce the development and performance evaluation of the HS‐MLC. The evaluation includes Monte Carlo simulations of the basic dosimetric properties, camera‐based measurements of the mechanical properties and tracking experiments for 25 sets of patient‐measured motion data. The Monte Carlo simulation results show that the maximum leakage at 6MV is 1.29% and the average is 0.61%. The end‐to‐end leakage is 3.96% for 5 cm offset and is 1.75% for 10 cm offset. The penumbra for a standard 10 × 10 cm2 field ranges from 4.8 mm to 5.4 mm across the full range of leaf motion. The mechanical property measurements demonstrate that the maximum leaf speed is 40 cm/s, the maximum leaf acceleration is 1000 cm/s2, and the geometric accuracy can be kept within 0.5 mm. Regarding the tracking experiments for a wide range of motion patterns (fast breathing, irregular breathing, etc.), a root‐mean‐square error (RMSE) of less than 0.19 mm was achieved. In conclusion, the HS‐MLC is able to well track fast target motion that is beyond the capability of conventional MLCs due to its superior mechanical properties. The new MLC design provides a feasible solution to make high‐accuracy and high‐efficiency motion management possible.


| INTRODUCTION
In radiotherapy, intrafractional motion induced by respiration may cause large discrepancy between delivered and planned dose distributions. 1 Several techniques accounting for intrafractional motion have been proposed, including motion encompassing, respiratory gating, multileaf collimator (MLC) tracking, etc. 2 Among them, MLC tracking is realized through dynamically adapting the aperture to the moving target, which does not rely on margin enlargement or beam hold-offs (unless large position error occurs) in contrast to the first two. Previous studies have applied MLC tracking to dealing with different forms of target motion: one-dimensional (1D) translation, [3][4][5][6] two-dimensional (2D) translation, [7][8][9] three-dimensional (3D) translation, 10 rotational motion 11 and deformation. 12 Plenty of studies have pointed out that limited leaf speed/acceleration is a major constraint to tracking capability. [13][14][15][16] To keep up with a moving target, the maximum leaf speed should at least exceed the maximum target speed in the case of target motion parallel to leaf direction. Moreover, the requirement for maximum leaf speed is much higher in the case of target motion perpendicular to leaf direction. 13,17 Conventional MLCs typically have a maximum leaf speed of 3-4 cm/s, 18 whereas the target motion is likely to exceed this speed and even can reach up to 9.4 cm/s. 19 Therefore, for conventional MLCs, tracking fast target motion is beyond their capability, especially when the perpendicular component is large. Beam hold-offs occur when the position error exceeds the machine tolerance, which inevitably sacrifices efficiency.
To remove or reduce violation of the MLC mechanical constraint -namely the occurrence of beam hold-offs, several software-based efforts have been made to date, such as optimal leaf sequencing algorithm 4,7,14 and moving average algorithm. 15 Nevertheless, there still remain some limitations using these algorithms. An alternative solution is to optimize structure of MLC to achieve higher leaf speed/acceleration. For conventional MLCs, the leaf speed/acceleration is limited mainly because the rotary motors adopted cannot provide adequate torque. One way to increase the torque is to adopt new rotary motors with larger power. But this is probably not allowed because larger power rotary motors require larger installation space. An alternative way is to replace rotary motors with other variants. The binary MLC employs air cylinders to drive leaves, achieving an extremely fast speed of around 2.5 m/s (slice thickness, 5 cm; switching time, 20 ms). 20 However, the binary MLC has only two states-wide open and fully closed because it was first designed for tomotherapy only.
To simultaneously achieve the two goals, that i, high leaf speed/ acceleration and continuous leaf trace control, we have recently developed a novel high-speed multileaf collimator (HS-MLC) prototype, which employs linear motors as the drive elements. Linear motors are especially well known for the advantages of direct drive and high dynamics, which provide the possibility to increase leaf speed/acceleration considerably. This paper mainly aims to introduce the development and performance evaluation of the standalone HS-MLC which is a non-integrated non-radiated newly developed MLC system. First, the description of the HS-MLC and position measure-    Table 1. Each leaf is driven by a linear motor, which consists of a stator (made of coils) and a mover (made of magnets). The electro-magnetic interaction between the stator and the mover produces axial thrust force directly. The mover is mechanically connected to either the body of the leaf or the extended portion of the leaf through a rigid bar (see the right side of Fig. 1). No transmission mechanisms such as gear-rack or screw-nut are needed to convert rotation to linear motion. The leaf position is detected through a position sensor mounted inside the linear motor.

2.A.2 | Control framework of the HS-MLC
The framework of the control system is shown in Fig. 2. It mainly consists of a master station (embedded PC) and 32 slave nodes (microprocessors). Each slave node controls 4 linear motors based on the controller. The EtherCAT bus is adopted as the bridge between the master station and the slave nodes benefiting from its high transmission rate (maximum transmission rate, 100 Mbit/s) and highaccuracy clock synchronization (less than 1 ls). In addition, the three data flow paths (processing path, reverse path, and detection path) can be clearly seen from

2.A.3 | Camera-based position detection method
A camera-based measurement system (Sony HDR-CX520) was constructed to evaluate the mechanical properties (see Fig. 1). This measurement technique was first adopted by Keall et al. 21 and Sawant et al. 10 to evaluate the geometric accuracy of a DMLC tracking system. To facilitate the subsequent image processing, a green plate with a cross-mark was placed under the aperture (see Fig. 3). The frame rate of the camera is 25 Hz, which means the interval between two image frames is 40 ms. Each image frame contains 1920 9 1080 pixels. Adjust the camera's field of view to 9.6 9 5.4 cm 2 , which corresponds to a resolution of 0.05 mm. As the geometric dimension of the cross-mark is known in advance, it is used as a standard to calibrate the leaf position in case that the camera's field of view is not exact. A Matlab program was developed for the image processing, as illustrated in Fig. 3. Step 1: extract a RGB image from the video.
Step 2: convert it to a grayscale image (extract the green channel of the RGB image).
Step 3: locate the central line of the leaf.
Step 4: plot the "pixel value versus x coordinate" curve.
Considering that the colors of the leaf and the plate contrast against each other greatly, the curve changes abruptly at the intersection between the leaf and the plate. However, due to the impact of the rounded leaf end and the shadow, it is difficult to determine which point on the curve is exactly the leaf tip. We use the first turning points of adjacent image frames to calculate the relative leaf position, rather than the absolute leaf position. Through this way, the systematic error is eliminated. For further validation, the comparison between the camera and the inbuilt position sensor was made, as shown in

2.C | Evaluation of the mechanical properties
The evaluation of the mechanical properties involves the maximum leaf speed and maximum leaf acceleration, geometry accuracy and the capability of the HS-MLC in tracking target motion. For each measurement, a leaf sequence file was generated and then transmitted to the master station. Once the file was executed, the actual trajectories of the selected leaves were extracted from the camera-  Step 4 Step 1 Step 2 Step 3 Steps of imaging processing. The bottom panel compares the outputs of the camera and the inbuilt position sensor.
created (see Fig. 5(a)). Such a request was far beyond the capability of the HS-MLC. In the absence of acceleration and maximum leafvelocity constraints, as a consequence, the leaf would first speed up to the maximum speed V max at full acceleration A max and then maintain this speed. Through this way, both V max and A max could be determined. As the acceleration period was very short, the inbuilt position sensor was used for this measurement instead of the camera on account of the finite frame rate of the camera.

2.C.2 | Geometric accuracy
The geometric accuracy includes two aspects: static accuracy and

3.A | Dosimetric properties
As seen in Fig. 9(a), the maximum leakage through the leaves is 1.8% and 1.5% of Varian Millennium MLC-120 (Varian Medical Systems, Inc., Palo Alto). 26 The results meets IEC (International Electrotechnical Commission) 27 requirement which allows a maximum of 2% and an average of 0.75%. The end-to-end leakage is 3.96% at 5 cm off-axis distance and is 1.75% at 10 cm offset, as seen in Fig. 9(b). For a standard 10 9 10 cm 2 field, the 80%/20% penumbra ranges from 4.8 mm to 5.4 mm across the full range of leaf motion, as seen in Fig. 9(c). The penumbra profiles for different field sizes (5 9 5 cm 2 , 10 9 10 cm 2 , 15 9 15 cm 2 , 20 9 20 cm 2 ) are displayed in Fig. 9(d), showing that the 80%/20% penumbra varies from 5.0 mm to 5.9 mm.   leaf to move at the maximum acceleration A max until the maximum speed V max was reached. As shown in Fig. 5(a), after the command signal given to the HS-MLC, it maintains stationary in several control cycles and does not respond to the command signal simultaneously.
However, the mechanical latency is less than 5 ms based on the local enlarged drawing. In consideration of the fluctuation of the actual speed (see green dash line in Fig. 5(b)), a fitting curve composed of two segments was constructed (see red dash dot line in Fig. 5(b)). Accordingly, A max was equal to the slope of the first segment, that is, 1212 cm/s 2 , and V max to the amplitude of the second segment, that is,. 42.6 cm/s. Their nominal values were determined to be 1000 cm/s 2 and 40 cm/s, respectively.   with the increase in the frequency, the RMSE tended to be larger.

3.B.3 | Leaf-leaf variations
A comparison of the actual trajectories of 32 adjacent leaves of right bank B when following the same 0.8 Hz sinusoidal trajectory is shown in Fig. 11. The average leaf deviation (see green triangle in  MLCs. This is guaranteed by two factors. On one hand, rigid rods are used to connect the linear motors and the leaves rather than gear-rack or screw-nut mechanisms such that the mechanical backlash is eliminated thoroughly. On the other hand, the Ether-CAT bus is adopted as the interface between the master station and the slave nodes, which allows a short control cycle and introduces little latency into the system. be noted that the regular breathing trajectory in Fig. 11(a) is approximated to a sinusoidal trajectory with frequency of 0.25 Hz. We compared the RMSE with that in Fig. 9(b): the former had lower leaf speed but the same level of tracking error existed. This result violated the aforementioned trend because the control cycle was increased from 1 ms to 33.3 ms here to match the sampling rate. Thus, the control points were less and as a result the control performance was decreased.

3.C | Performance of tracking target motion
Further development and promotion of the HS-MLC is still in progress and several issues remain to be addressed.

1.
With some hardware and software modifications, there is still a great potential to further promote performance of the HS-MLC.
The linear motors can provide higher thrust force by increasing their current, but at the expense of producing more heat. This needs a stronger cooling system to avoid overheating of the linear motors. The geometric accuracy, on the other hand, can be increased through the following aspects. First, since the geometric accuracy is mainly subjected to the friction of the guide, better coating material and better lubricant are required. Second, by combining the adopted proportion-integration-differentiation (PID) control algorithm with other advanced algorithms, better control performance can be achieved. In addition, for discrete motion data with a low sampling rate, it is necessary to insert more control points between two sampling points to improve the control performance.
2. The HS-MLC was evaluated as an independent system in this paper. It is available to be integrated into an accelerator to evaluate its overall performance since the prototype HS-MLC was within clinical requirements according to the IEC regarding MLC on a linac. Actually, to examine the mechanical and dosimetric performance, the prototype MLC can be mounted on a selfdeveloped linear accelerator whose source to axis distance (SAD) and source to collimator distance (SCD) are 1000 mm and 380 mm, respectively. Based on the schematic of the collimator head in the linac, as illustrated in Fig. 12, the collimator head involved two groups of adjustable opposing tungsten alloy blocks Schematic description of MLC position in the head.
(X1, X2, Y1, and Y2 in Fig. 12). With the aim of reducing the interleaf leakage and leaf transmission in IMRT treatments, both of them are located above the MLC leaves. Furthermore, each individual block implements the same mechanism of rack and track system for movement and can be separately driven by an electric motor.
Considering incorporation with the collimator head, the influence of the sag in linac secondary collimator and MLC carriage on delivery quality should be explored. To implement tracking tasks in practice, it also should be incorporated with imaging system and it is necessary to investigate whether the image acquiring accuracy and the latencies from other subsystems may impair the tracking performance. 28,29 3. Only target motion parallel to the leaf motion direction is considered in this paper. Under this assumption, the HS-MLC can achieve 100% efficiency due to the fact that the achieved maximum leaf speed (40 cm/s) far exceeds the maximum target motion speed (9.4 cm/s, reported by Shirato et al. 2006). 19 However, the other forms of target motion also widely exist. It has been reported that large perpendicular translational motion 10 and large rotational motion 11 are likely to cause very low efficiency.
Therefore, it is worth studying whether the HS-MLC is capable to compensate for other forms of target motion without loss of efficiency.

4.
When the HS-MLC is used for intensity modulated radiotherapy therapy (IMRT) treatments, how to maximize its performance is a crucial problem. The leaf motion in IMRT serves two functions: one for delivering the IMRT plan, the other for synchronizing with the target motion. This raises a question about how to allocate the maximum leaf speed between the two functions. Allocating more to the former contributes to reducing monitor units, treatment time and given radiation dose to organs at risk; 30,31 allocating more to the latter allows tracking faster target motion.
Therefore, the allocation strategy needs to be well optimized to balance the two functions.
In conclusion, with superior mechanical properties, the HS-MLC is highly promising for high-accuracy and high-efficiency motion management in the future.

CONF LICT OF I NTEREST
The authors have declared that no conflict of interest exists.